The Virtual Surjection Conjecture for Discrete Groups

If a subgroup of a product of groups of type $F_k$ virtually surjects onto every $k$ -tuple of factors, must it be of type $F_k$ itself? Yes, for discrete groups, and likewise for $FP_k$ . The homological $n$ - $(n+1)$ - $(n+2)$ Conjecture follows for discrete groups when the common quotient is finitely presented, and that hypothesis cannot be dropped.

Result: Proved
Status: Resolved
AI contribution: AI co-developed
Method: Argument
Field: Geometric group theory
Posed by: Martin Bridson, James Howie, Charles Miller III, Hamish Short
Year posed: 2013
Years open: 13y
Solved: 2026-07-20
Model: GPT
Vendor: OpenAI
Collaborators: Tal Cohen, Mark Shusterman
Verification: Unreviewed
Publication: Preprint
Significance: 20 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

The authors write that they developed the main arguments in the body of the paper in the course of interactions with GPT. The disclosure does not break the contribution down further.

Verification

arXiv preprint; not yet peer-reviewed.

Source

arXiv:2607.18079 - Virtual Surjection and the n-(n+1)-(n+2) Theorem for Discrete Groups

The Virtual Surjection Conjecture for Discrete Groups

What the AI did

Verification

Source

Discussion